This set of Aptitude Questions and Answers (MCQs) focuses on “Height and Distance – Set 2”.

1. From a point Q on a level ground, the angle of elevation of the top tower is 53 degree. If the tower is 150 m high, then what is the base distance of point Q in m?

a) 200 m

b) 225 m

c) 112.5

d) 150 m

View Answer

Explanation: Given,

Height = 150 m, angle = 53 – degree

Let the base distance = x m.

➩ tan 53 = height / base distance

➩ 4 / 3 = 150 / x

➩ x = 150 * 3 / 4 m

➩ x = 112.5 m

2. The angle of elevation of a ladder leaning against a wall 37 degree and the foot of the ladder is 5 m away from the wall. What is the length of the ladder?

a) 25 / 4 m

b) 25 / √3 m

c) 50√2 m

d) 50 / 4 m

View Answer

Explanation: Given,

Angle = 37 – degree, base distance = 5 m

Let the length of the ladder = h m.

➩ cos 37 = base distance / length of ladder

➩ 4 / 5 = 5 / h

➩ h = 25 / 4 m

3. An observer 1.5 m tall is 10√3 m away from the tower making an angle of elevation of 60 degree from his eyes. What is the height of the tower?

a) 60 m

b) 31.5 m

c) 30 m

d) 63 m

View Answer

Explanation: Given,

Angle = 60 – degree, base distance = 10√3 m

Let the height of the tower above the man be = h m

➩ tan 60 = height / base distance

➩ √3 = h / 10√3

➩ h = 30 m

Thus, height of the tower = 30 + 1.5 m

= 31.5 m

4. What is the angle of elevation (in degree) of the sun, when the ratio of the length of the shadow of a tree to height of the tree is 3:4?

a) 37

b) 45

c) 53

d) 60

View Answer

Explanation: Let the angle be = x degree.

According to the question,

➩ tan x = 3 / 4

➩ x = 37 degree

5. The angle of depression of a point situated at a distance of 50 m from the base of the pole is 45 degree. What will be the height of this pole?

a) 50 / √3 m

b) 25√3 m

c) 50 m

d) 25√2 m

View Answer

Explanation: Given,

Angle = 45 – degree, base distance = 50m

Let the height of the pole be = h m.

➩ tan 45 = height / base distance

➩ 1 = h / 50

➩ h = 50 m

6. The angle of depression of a car, standing on the ground, from the top of a 100 m tower is 37 degree. What is the base distance (in m) of the car?

a) 200√3 m

b) 400 / √2 m

c) 300 / 4 m

d) 400 / 3 m

View Answer

Explanation: Given,

Height = 100 m, angle = 37 degree

Let the base distance be = b m.

➩ tan 37 = height / base distance

➩ 3 / 4 = 100 / b

➩ b = 400 / 3 m

7. The angle of depression of two ships from the top of a light house are 45 and 30 degree, sailing in the same direction. If the height of the light house is 150 m, then what will be the distance between the 2 ships?

a) 150 (√3 – 1) m

b) 150√3 / 2 m

c) 150√2 / 3 m

d) 150 (√2 – 1) m

View Answer

Explanation: Given,

Angle of X ship = 45 – degree, angle of Y ship = 30 – degree, height = 150m

Let the distance between ship X and glacier be x m, ship Y and glacier be y m.

Ship X

➩ tan 45 = height / base distance

➩ 1 = 150 / x

➩ x = 150 m

Ship Y

➩ tan 30 = height / base distance

➩ 1 / √3 = 150 / y

➩ y = 150√3

Distance between the two ships = y – x

= 150√3 – 150 m

= 150 (√3 – 1) m

8. A skier took 60 s to travel down a snowy slope of vertical height 200 m. If the angle of depression is 45 degree, then what will be the speed of the skier in m / s?

a) 5.62 m / s

b) 5.32 m / s

c) 4.66 m / s

d) 4.02 m / s

View Answer

Explanation: Given,

Angle = 45 – degree, perpendicular height = 200 m, time taken = 60 s.

Let the distance traversed = x m.

➩ sin 45 = perpendicular / hypotenuse

➩ 1 / √2 = 200 / x

➩ x = 200√2 m

Speed = distance / time = (200√2) / 60 = 4.66 m / s

9. A ball is placed 50 m away from the wall of a pool. The angle of depression of the ball from the pool platform is 37 degree, then what will be the diagonal distance he will have to swim to get the ball?

a) 44.5m

b) 82.5 m

c) 62.5 m

d) 78.5 m

View Answer

Explanation: Given,

Angle = 37 – degree, base = 50 m

Let the diagonal distance = d m.

➩ Cos 37 = base / diagonal

➩ 4 / 5 = 50 / d

➩ d = 62.5 m

10. A straight tree is broken due to thunder storm. The broken part is bent in such a way that the peak touches the ground at an angle elevation of 45°. The peak of the tree touches the ground at a distance of 25 m. What will be the height of the tree?

a) 25(1 + √2) m

b) 20√3 m

c) 25 / √3 m

d) 22√2 m

View Answer

Explanation: Given,

Angle = 45 – degree, base distance = 25 m.

Let the vertical height be = x m, diagonal length be = y m.

➩ tan 45 = vertical height / base distance

➩ 1 = x / 25

➩ x = 25 m

Also,

➩ sin 45 = vertical height / perpendicular distance

➩ 1 / √2 = 25 / y

➩ y = 25√2 m

Height of the tree = x + y

= 25 + 25√2 m

= 25(1 + √2) m

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